Mean magnitude variations of earthquakes as a function
of depth: Different crustal stress distribution depending
on tectonic setting
M. Wyss, F. Pacchiani, A. Deschamps, G. Patau
To cite this version:
M. Wyss, F. Pacchiani, A. Deschamps, G. Patau. Mean magnitude variations of earthquakes
as a function of depth: Different crustal stress distribution depending on tectonic setting.
Geophysical Research Letters, American Geophysical Union, 2008, 35 (1), pp.L01307. . .
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GEOPHYSICAL RESEARCH LETTERS, VOL. 35, L01307, doi:10.1029/2007GL031057, 2008
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Mean magnitude variations of earthquakes as a function of depth:
Different crustal stress distribution depending on tectonic setting
M. Wyss,1 F. Pacchiani,2 A. Deschamps,3 and G. Patau4
Received 20 June 2007; revised 7 September 2007; accepted 10 December 2007; published 15 January 2008.
[1] The mean magnitude of earthquakes in the Gulf of
Corinth is found to increase strongly with depth (b-value
decreases), whereas the dip of fault planes decreases. The bvalue difference of 0.25, between shallow and deep
earthquake distributions, is based on about 7,000 events
and therefore is statistically highly significant. The same is
true in California, but opposite patterns are observed in
southern Iceland and in western Nagano, Japan. Because
large mean magnitudes (low b-values) are indicative of
relatively high stress levels, we propose that in the
detachment layer at about 9 ± 2 km depth, earthquakes
are generated at higher stresses than in the shallower
parts of the crust. The correlation of low b-values with
low faulting dips can be taken as line of evidence that low
b-values map high stress regimes. Citation: Wyss, M.,
F. Pacchiani, A. Deschamps, and G. Patau (2008), Mean
magnitude variations of earthquakes as a function of depth:
Different crustal stress distribution depending on tectonic setting,
Geophys. Res. Lett., 35, L01307, doi:10.1029/2007GL031057.
1. Introduction
[2] We map the local mean magnitude of earthquakes, M ,
using the b-value, by equation (1) [Aki, 1965]
b¼
1
;
2:3 M Mmin
2. Data
ð1Þ
where Mmin is the minimum magnitude in the local data and
b is the slope of the linear fit to the frequency-magnitude
distribution, FMD,
log N ¼ a bM ;
[4] M is proportional to the ambient stress in the local
seismogenic volume (and by equation (1), b is inversely
proportional to stress). Scholz [1968] has shown this in the
laboratory for microfractures and has proposed a model
explaining this phenomenon. The evidence that local bvalues of earthquake distributions are inversely proportional
to the ambient stress is the following: (1) b-values of the
earthquakes triggered by pumping of fluids into the crust at
Denver tracked the volume of liquid injected [Wyss, 1973].
(2) In underground mines, b-values were found to be
inversely dependent on the stress level [Urbancic et al.,
1992]. (3) Known asperities along the San Andreas fault
show low b-values [Schorlemmer et al., 2004; Wiemer and
Wyss, 1997]. (4) Increases of b-values that correlate with
magmatic intrusions are best explained by increases of pore
pressure [Wiemer et al., 1998]. (5) High, medium and low bvalues correlate worldwide with normal, strike-slip and
thrust faulting, respectively [Schorlemmer et al., 2005].
[5] To identify differences in stress level, we investigate
differences in b-values, presenting the newly discovered
decrease of b-values (increase of M ) with depth in the
western Gulf of Corinth and comparing this pattern with
patterns observed in Iceland, California and Japan.
ð2Þ
where N is the cumulative number of events and a is a
constant that measures the seismicity rate.
[3] We discuss b-values instead of M to compare the
distribution of M in data sets from several seismograph
networks that work at different resolutions, i.e. different
Mmin. Thus, comparisons of b-values can be easily understood, whereas values for M may be meaningless for the
reader.
1
World Agency of Planetary Monitoring and Earthquake Risk
Reduction, Geneva, Switzerland.
2
Laboratoire de Géologie, Ecole Normale Supérieure, Paris, France.
3
Geosciences Azur, Université of Nice Sophia Antipolis, Centre
National de la Recherche Scientifique/Pierre and Marie Curie University/
Institut de Recherche pour le Développement, Valbonne, France.
4
Département de Sismologie, Institut de Physique du Globe Paris, Paris,
France.
[6] The French national project GDR-Corinthe and the
international projects CORSEIS and 3HAZ (crl.ens.fr/metadot)
have operated a 12-station seismograph network since 2001
in the western Gulf of Corinth [Lyon-Caen et al., 2004]. The
stations are typically positioned 5 km apart.
[7] We mapped Mc, using the best combination method
in zmap [Wiemer, 2001], starting with a large area, reducing
it in steps. For each volume, we also calculated Mc as a
function of time. Before selecting the final volume for
analysis, we mapped Mc in cross section. In addition, we
plotted the ratio of events recorded during nighttime to
those recorded during daytime. These latter plots were
helpful in verifying that for small Mmin, fewer events were
reported during the day than during the night. An Mc = 1.3
leads to the best compromise for selecting the extent of
good quality data in space and time and it leads to constant
reporting during nighttime and daytime. Mapping Mc, we
defined an area of about 25 km in diameter, centered on the
network, that is complete at M = 1.3 out to the edges and to
a depth of 15 km. At the center of this area, Mc is 1.1, and
the ratio of nighttime to daytime events is nearly constant.
Estimating Mc as a function of time revealed that the
network experienced a period of buildup, during which
resolution was poor. After the date of 2001.3, Mc was
stable at 1.3. A search for explosions yielded none.
Copyright 2008 by the American Geophysical Union.
0094-8276/08/2007GL031057$05.00
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depth most clearly. For each case, the homogeneity of
reporting had been reviewed by the respective authors.
The errors in depth estimates are less than 1.5 km in these
catalogs.
3. Results
Figure 1. Cross section, 10 km wide, across the Corinth
Gulf showing the best located hypocenters of earthquakes
with M 1.3, recorded between 2001.3 and 2006.2. The
black lines schematically depict the fault structure inferred
from the geometrical analysis of relocated multiplets. The
dotted line represents the transition zone between high and
low angle dipping multipelts. The star marks the hypocenter
of the M6.2 Aigion earthquake, of 15 June 1995. The data
including all events with M 1.1 contain 5.5 times more
earthquakes.
[8] We performed the analysis that follows using three
catalogs, all for the period 2001.3 to 2006.2. For the most
general analysis, we used events with M 1.1, located
down to a depth of 20 km (16,303 events), for a more
restricted analysis, we used those with M 1.3 and located
at depths of less than 15 km (7,102 events). Finally, the
analysis was repeated using only earthquakes with high
quality locations, defined as events, which were located
with at least three P-wave and three S-wave phases, had an
rms less than 0.4 sec and absolute standard errors less than 2
km in x, y, z. In the data set of high quality locations, the
minimum magnitude of completeness was elevated to Mc =
1.4. The number of events whose magnitude is equal to and
larger than M1.4 was 2,155 (when M 1.3 were included
the number of events was 3,090). All data sets, with all
aforementioned selections of Mc, yielded the same results,
overall, with some details differing by small amounts.
During the period covered, the largest earthquake had M =
3.8. The best located hypocenters used for b-value analysis
and specified above are shown in Figure 1.
[9] The data used for comparison with the results from
the Gulf of Corinth are the following. For southern Iceland,
the catalog covering the volume containing the main shocks
of M6 in 2000 and described in detail by Wyss and
Stefansson [2006] was used. For Parkfield, the special
high-accuracy catalog analyzed by Wyss et al. [2004] was
used. For the Tokai-Kanto area, the catalog previously
analyzed by Wyss and Matsumura [2002, 2005] was
employed. In that catalog, the b-value increases with depth
in the over-all data, however, details of the pattern vary as a
function of location. Here we selected a subset of the data
from western Nagano that shows the increase of b with
[10] Although the b-values are heterogeneous, varying
between about 1 and 2.2 on a scale of approximately 2 km,
they are predominantly high in the shallow layers and low
in the deeper layers (Figure 2). We estimated the statistical
significance of the difference of b between shallow and
deep parts, using Utsu’s [1992] test. The difference was
significant at divisions at any depth between 5.5 and 10 km,
but there is a clear contrast between cuts above and below
7 km. When cutting above 7 km, the probability that the two
samples come from the same population ranges from 103
to 7 103, whereas for cuts below 7 km the probabilities
range from 2 105 to 2 104. The lowest value is reached at
a cutting depth of 9 km. Thus, we conclude that the b-value
decreases somewhat gradually with depth (Figure 3a), and
the contrast between shallow and deep parts is expressed
most strongly, if one cuts at 9 ± 1 km depth.
[11] For plotting the maps, samples were taken with N =
100 events at nodes of grids with a separation of 1 km. For
the cross section, the node separation was the same and
samples of N = 200 were used. In each sample, the
minimum magnitude of completeness was automatically
re-evaluated before estimating b. For samples where fewer
than 50 events (80 events alternatively) were available for
the determination of b (considering the local Mc and
discarding events with M < Mc), the calculation was not
performed. The analysis was also carried out, using constant
radii of sizes that yielded approximately 100 to 200 events
per sample (r = 2, 2.5 and 3 km, respectively). The visual
appearance of the maps and cross sections was the same
using the varied selection criteria.
[12] The average b-value as a function of depth in the
Gulf of Corinth (Figure 3a) decreases from about 1.6 to a
minimum of 1.2 at 10 km. Thus, at a depth of 8 to 12 km,
proportionally more medium size earthquakes are produced
than at other depths. This pattern is similar to the increase of
mean magnitude (decrease of b) with depth found in
California, for which area, Gerstenberger et al. [2001]
performed a detailed analysis. Here, we confirm the previous results for California with a different data set that shows
a decrease of b with depth near Parkfield, where a catalog
with highly precise hypocenters exists (Figure 3c).
[13] In southern Iceland, the pattern is reversed: at depths
shallower than 5 km b = 0.6, whereas b = 0.9 below 7 km
depth (Figure 3b). The data shown in Figure 3b are the
aftershocks of the two M6.6 main shocks of 2000. This data
set covers a different period than the data used by Wyss and
Stefansson [2006], who had previously also shown that b
increases with depth in southern Iceland. Wyss and
Matsumura [2002] have shown that the b-values increase
with depth in the Tokai-Kanto, Japan, area. Similar to
Gerstenberger’s findings in California, the pattern in Japan
is not everywhere the same. In Figure 3d, we show an
example from western Nagano where the average b increases
gradually with depth from 0.6 to 1.3.
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Figure 2. Maps of b-value in volumes with N = 100 events (a) above and (b) below 8 km. (c) Cross section from point
38.37N/21.95E to point 38.22N/22.25E, 20 km wide, showing b in volumes with N = 200 events. Coastlines are shown as
solid black lines, fine lines demark the bathymetry. The catalog used included all events with M 1.1. The shape of the
sampling volumes was a cylinder with fixed height and varying radii.
[14] In order to verify that the differences are statistically
significant, and to present the appearance of the frequency
magnitude distribution (FMD) we compared the average
FMD plots of shallow events with deeper ones for each area
(Figure 4). These difference are judged highly significant by
Utsu’s [1992] test, which we performed for a number of
depth cuts. Given that the differences in b are typically
0.3 units and the numbers of events in each sample exceed
1,000, the probability that the compared samples come from
the same population is invariably below 103.
4. Discussion
[15] The tectonic process that generates earthquakes in
the Gulf of Corinth is rifting in a NE-SW direction. GPS
measurements show an extension rate of about 1.5 cm/year
[Briole et al., 2000; Bernard et al., 2006] that is modeled by
near-horizontal slip along the detachment plane shown in
Figure 1 at about 8 km depth [Bernard et al., 2006].
[16] In Iceland, the overall regime is also one of rifting,
but in the southern Iceland seismic zone, the major earthquakes occur along near-vertical, N-S trending strike-slip
faults [Einarsson, 1991]. The number of earthquakes
increases steadily as a function of depth and drop abruptly
below 10 km.
[17] In western Nagano, Japan, the faulting in the shallow
crust takes place primarily as strike-slip on near-vertical
planes in response to the EW compression due to underthrusting of the oceanic plates located east of Japan. Here
the seismicity continues to depths greater than shown for
comparison. The activity peaks at 10 km depth.
[18] Along the strike-slip fault segment at Parkfield, most
earthquakes occur near 4 km depth, with minor peaks of
activity at 7 and 9 km. Here, as in all of the data sets, the
data from the mapped asperities and creeping sections were
mixed for the overall analysis performed as a function of
depth. Previously, Gerstenberger et al. [2001], using the
USGS data, found that b decreased with depth in general,
but not everywhere. Similar heterogeneities were found in
all the data sets analyzed. In Figures 1 – 4 we present the
prevalent trends. Gerstenberger et al. [2001] interpreted
their observation as due to the increase of confining stress
with depth.
[19] We propose that a similar mechanism of elevated
stress is at work in the Gulf of Corinth leading to an
increase of M with depth to 10 km (Figure 3a). Pacchiani
[2006] relocated multiplets with high accuracy and was able
to map the geometries of the fault planes on which the
events occurred. He found that above 8 km depth the dips of
the fault planes were relatively steep (60° on average) and
below 8 km their dip was shallower (30°on average) (Figure 1).
Thus, the overburden tends to clamp shut the faults at depth
greater than 8 km and hence elevated shear stress is required
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Figure 3. The b-values as a function of depth in overlapping samples of N events. For the Gulf of Corinth, only events
with high quality hypocenter estimates and M 1.4 were used. Error bars are calculated according to Shi and Bolt [1982].
The error bars do not overlap, and thus confirm the statistical significance of the difference between samples, elsewhere in
this work estimated by the method of Utsu [1992].
to rupture these low angle faults, especially the detachment
fault modeled by Bernard et al. [2006].
[20] At the very bottom of the seismicity in the Gulf of
Corinth, the b-values increase (Figure 3a), suggesting that at
the lower limit of the seismogenic layer faulting may occur
under reduced stresses. This may be interpreted as due to
elevated temperatures at the transition from brittle to ductile
crust, which may allow faulting at reduced stresses.
[21] Our conceptual model for explaining the distribution
of seismicity and mean magnitude with depth is as follows:
[22] 1. There are no earthquakes in the top few kilometers
of the crust in any of the areas studied and Labaume et al.
[2004] demonstrate extensive fluid processes in and around
the fault planes in the Corinth rift at 1 to 2 km depth. We
interpret this to mean that at shallow depths low normal
stresses and pore pressures preclude build up of stress to the
point of rupture by earthquakes. Deformation presumably
takes place a-seismically [Bernard et al., 2006].
[23] 2. The maxima of mean magnitude, demonstrated
here to occur between 8 and 11 km depth beneath the Gulf
of Corinth, suggests that stresses are concentrated there and
main asperities from which main shocks are likely to
emanate, are located at these depths. This agrees with
relocations of hypocenters of the larger earthquakes in the
Corinth rift by waveform modeling. For the M6.9 earthquake of 1981 in the eastern part of the rift, Jackson et al.
[1982] found a hypocentral depth of 10 ± 2 km, for the
M5.7 earthquake of 1992 (at the edge of the area studied
here) the relocated depth was 7.4 ± 1 km [Hatzfeld et al.,
1996], and for the M6.2 earthquake that occurred in 1995 in
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Figure 4. Cumulative numbers of earthquakes as a function of magnitude for the same areas as used in Figure 3. In each
case, a shallow data set (open squares) is compared with a deeper one (solid triangles). For the Gulf of Corinth, b = 1.55 ±
0.06 and b = 1.16 ± 0.04 for shallow and deep samples, respectively, where the errors are calculated according to Shi and
Bolt [1982].
the study area, Bernard et al. [1997] found a depth of 10 ±
3 km.
[24] 3. In the depth range of 4 to 7 km, seismicity exists,
but is limited to smaller events than at depth and occurs
along faults with steep dips at intermediate stress levels.
[25] The pattern of increasing b-values with depth observed in Iceland was interpreted as due to increasing pore
pressure [Wyss and Stefansson, 2006] that allows faulting
under lower stresses. This interpretation seemed attractive
because various arguments had been put forth by other
researchers that pore pressure increases with depth in
southern Iceland [e.g., Stefansson and Halldórsson, 1988].
We do not know whether the same interpretation might be
valid in Nagano. Currently, not enough areas have been
examined in detail for establishing details of trends of mean
magnitude with depth and along fault zones. Our results that
reveal an increase of mean magnitude with depth in the Gulf
of Corinth area, once again show that detailed mapping and
analysis of b-values (or M ) have the potential of advancing
our understanding of faulting processes and stress distribution in the crust.
[26] We conclude that the increased mean magnitude of
earthquakes at depths of 8 to 10 km is further evidence that
main shocks are generally expected to emanate from these
depths in the Gulf of Corinth, and not from shallower
layers. The evidence presented here, that low b-values (large
M ) correlate with low dip angle of the fault planes, can be
taken as another line of evidence that supports the hypothesis that low b-values map high stress regimes.
[27] Acknowledgments. We thank H. Lyon-Caen for providing the
seismicity catalogs and S. Wiemer for his software zmap for analysis. We
thank anonymous reviewers for helpful comments. This research was
supported by the E.C. project 3HAZ-Corinth (contract GOCE 004043).
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A. Deschamps, Geosciences Azur, Université of Nice Sophia Antipolis,
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